A modulated point-vortex model for geostrophic, β-plane dynamics
A modulated point-vortex model for geostrophic, β-plane dynamics
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地转 β 平面动力学的调制点涡模型
DOI：
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发表时间：
1982
期刊：
影响因子：
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通讯作者：
J. McWilliams
中科院分区：
文献类型：
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作者：
N. Zabusky;J. McWilliams
提出了一种新的调制点涡模型，用于等效位涡正压方程：qt−ψyqx +ψxqy=0, (q=κ+βy, κ=∇2ψ−γψ)。离散模型守恒 Σm(qm0 −β*ym)2 ，与守恒 ∫ ∫κ2 dx dy 类似。对一般的两点涡系统进行了分析研究。对于相等的涡流，解具有单调漂移 ∝(−β)。对点涡模型的数值解和周期域上有限差分模型的相应解进行了比较。对于 ∇2ψ−γ2ψ 的初始单极分布，在两种情况下都获得了在符号 (−β) 方向上的 x 漂移和在 κ 极值符号方向上的 y 漂移，并且在短时间内一致。根据守恒定律，y 漂移与罗斯贝波尾流传播的发展相关。对于“倾斜”的涡度偶极区域，我们观察到近周期振荡。调制点涡模型也适用于等离子体中的漂移波。
A new modulated point‐vortex model is presented for the equivalent barotropic equations of potential vorticity: qt−ψyqx +ψxqy=0, (q=κ+βy, κ=∇2ψ−γψ). The discrete model conserves ∑m(qm0 −β*ym)2 in analogy with the conserved ∫ ∫κ2 dx dy. An analytical study is made for the general two point‐vortex system. For equal vortices, the solution has a monotonic drift ∝(−β). A comparison is made of numerical solutions of the point‐vortex model and corresponding solutions of a finite‐difference model on a periodic domain. For an initially monopolar distribution of ∇2ψ−γ2ψ, an x drift in the direction of sign (−β) and a y drift in the direction of the sign of the extremum of κ is obtained in both cases that are in agreement at short times. The y drift is associated with the development of a spreading Rossby wave wake, as a consequence of the conservation law. For a ‘‘tilted’’ dipolar region of vorticity we observe near‐periodic oscillations. The modulated point‐vortex model is also applicable to drift waves in a plasma.